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Published in:
2015 | OriginalPaper | Chapter
Maximizing the Degree of (Geometric) Thickness-t Regular Graphs
Author : Christian A. Duncan
Published in: Graph Drawing and Network Visualization
Publisher: Springer International Publishing
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Abstract
In this paper, we show that there exist \((6t-1)\)-regular graphs with thickness t, by constructing such an example graph. Since all graphs of thickness t must have at least one node with degree less than 6t, this construction is optimal. We also show, by construction, that there exist 5t-regular graphs with geometric thickness at most t. Our construction for the latter builds off of a relationship between geometric thickness and the Cartesian product of two graphs.